Using optimal control to optimize the extraction rate of a durable non-renewable resource with a monopolistic primary supplier
| Autor: | Enric Fossas, Albert Corominas |
|---|---|
| Přispěvatelé: | Universitat Politècnica de Catalunya. Departament d'Enginyeria de Sistemes, Automàtica i Informàtica Industrial |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Mathematical optimization
Control and Optimization Informàtica::Automàtica i control [Àrees temàtiques de la UPC] Computer science Strategy and Management Optimització matemàtica Control Teoria de Upper and lower bounds Monopolistic competition Maximum principle Resource (project management) Control theory 49 Calculus of variations and optimal control optimization::49N Miscellaneous topics [Classificació AMS] Business and International Management Electrical and Electronic Engineering Monopoly Non-renewable resource Applied Mathematics Durable non-renewable resources Optimal control Atomic and Molecular Physics and Optics Time derivative optimization::49K Necessary conditions and sufficient conditions for optimality [Classificació AMS] Hamiltonian (control theory) |
| Popis: | The problem dealt with in this paper is that of optimizing the path of the extraction rate (and, consequently, the price) for the monopolistic owner of the primary sources of a totally or partially durable non-renewable resource (such as precious metals or gemstones) in a continuous-time frame, assuming that there is an upper bound on the extraction rate and with an interest rate equal to zero. The durability of the resource implies that, unlike the case of non-durable resources, at any time there is a stock of already-used amounts of the resource that are still potentially reusable, in addition to the resource available in the ground for extraction. The problem is addressed using the Maximum Principle of Pontryagin in the framework of optimal control theory, which allows identifying the patterns that the optimal policies can adopt. In this framework, the Hamiltonian is linear in the control input, which implies a bang-bang control policy governed by a switching surface. There is an underlying geometry to the problem that determines the solutions. It is characterized by the switching surface, its time derivative, the intersection point (if any) and the bang-bang trajectories through this point. |
| Databáze: | OpenAIRE |
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